Mailbox move with Cached Exchange Mode clients?

I am moving from an old Exchange 2003 server to a clean install on new hardware. Plan on using the "move mailbox" wizard in ESM. From what I've read it looks like it SHOULD be fairly smooth sailing, but I'm wondering about the clients. Most use Cached Exchange Mode and connect from outside the network (via RPC over HTTPs). I know how to reconfigure the registry keys on the new Exchange server and on the GC on the network to ensure RPC over HTTPs continues to function properly.

What I'm wondering though is if each user will be forced to redownload all of their email? In other words, will moving the mailbox to another server somehow invalidate their current OST file and force them to regenerate it? Since they're clients on the internet, that could really bog down the internet connection in the main office.

My hope is that it will just continue as it did before and only download changes to their mailbox since they last opened Outlook. Anyone done this before and can verify how it will behave?

"What I'm wondering though is if each user will be forced to redownload all of their email?"
No.
One thing to beware of is that if the new server's port 443 is not yet published to the internet (on the same public IP as the old server), the old server will need to function as a Front End server, so it acts as a proxy for the mailboxes that are hosted on the new server.

Correct, I'm doing all of the mailboxes at once and will then be reconfiguring port forwarding so that the hostname that's configured for them to connect to for RPC over HTTPs will point them to the new server.

Do you know if they'll have to go through the whole sync process again? I guess it makes sense that it wouldn't download all of the message all over again since it would already find them present on the client side. Now I'm wondering though if it's still going to scan all the contents of each mailbox folder. 50 people doing that at the same time (even if they don't end up having to actually download the message content) could still bog down the internet I would think.